The deconvolution of biological dielectric spectra can be difficult enough with artefact-free spectra but is more problematic when machine baseline artefacts and electrode polarisation are present as well. In addition, these two sources of anomalies can be responsible for significant interference with dielectric biomass measurements made using one- or two-spot frequencies. The aim of this paper is to develop mathematical models of baseline artefacts and electrode polarisation which can be used to remove these anomalies from dielectric spectra in a way that can be easily implemented on-line and in real-time on the Biomass Monitor (BM). We show that both artefacts can be successfully removed in solutions of organic and inorganic ions; in animal cell and microbial culture media; and in yeast suspensions of varying biomass. The high quality of the compensations achieved were independent of whether gold and platinum electrodes were used; the electrode geometry; electrode fouling; current density; the type of BM; and of whether electrolytic cleaning pulses had been applied. In addition, the calibration experiments required could be done off-line using a simple aqueous KCl dilution series with the calibration constants being automatically calculated by a computer without the need for user intervention. The calibration values remained valid for a minimum of 3 months for the baseline model and indefinitely for the electrode polarisation one. Importantly, application of baseline correction prior to polarisation correction allowed the latter's application to the whole conductance range of the BM. These techniques are therefore exceptionally convenient to use under practical conditions.